I have an 8 cell pack that I was hoping to put in a Zagi, but someone mentioned that the performance will likely be marginal. My question is...
How much current can I draw from these cells and what effect does a high current draw have on the pack?
Is the max draw determined by the size of the cell or the capacity of the battery or both?

There's no way to know how much current you can draw from the pack except by trial and error.

What determines how much current you can draw is how the cell was manufactured. Capacity and physical size are good indications, but they are not always accurate.

Take, for example, the typical AA NiMH. These are designed for maximum capacity, not for high current, since they're meant for use in digital cameras and children's toys. The manufacturer crams as much electrolyte and substrate into the cell as physically possible.

Think of a battery like a clown car; the more clowns in the car, the slower they have to move getting in and out to avoid hurting each other and damaging the car. If you put 16 clowns on a big roomy van (like a Sub C cell) they can pile out quickly, but if you stuff them into a VW Beetle (like a AA cell), you're going to be ripping off limbs trying to get them out quickly

Matt'a advice is good! One problem is that every brand of AA cell is different - I have seen published discharge rates for AA NiMh cells from different manufacturers and obviously of different construction, ranging from <1C up to >20C. A common figure seems to be 9C, but until you test YOUR cells you'll never know what they can produce.

The acid test:
Fly them for 5 min, land, and feel the packs. Are they hot? If not, fly for another 5 min and do the touch test again. If they are getting HOT, like I wouldn't want to hold those for very long, they probably won't last long. If they are just warm, fly away.
hoppy

the clown thing made me laff out loud.... pretty good analogy. I run the ol' RatShack 8 cell NiMh desiged for their RC cars and abuse them way too much on BL setups. They draw down pretty good and can keep a Mega running for a good 11-15 minutes on my AP wing.